loopy

"[...] the low-energy Hilbert space for n Fibonacci particles with trivial total topological charge has a dimension given by the (n-1)th Fibonacci number. Consequently, the asymptotic dimension per particle, usually called the quantum dimension, is the golden ratio φ = (1+sqrt(5))/2. Perhaps the most remarkable feature of Fibonacci anyons is that they allow for universal topological quantum computation in which a single gate---a counterclockwise exchange of two Fibonacci anyons---is sufficient to approximate any unitary transformation to within desired accuracy (up to an inconsequential overall phase)."

"[...] a 128-bit number can be factored in a fully fault-tolerant manner using Shor's algorithm with ≈10^3 Fibonacci anyons. In contrast, performing the same computation with Ising anyons [also non-Abelian but non-universal] would entail much greater overhead since the algorithm requires π/8 phase gates that would need to be performed nontopologically and then distilled [...]. For a π/8 phase gate with 99 % fidelity, the scheme [...] requires ≈10^9 Ising anyons to factor a 128-bit number."